Solving the Multi-Vehicle Inventory Routing and Management Integrated Problem Using Mixed-Integer Linear Programming

Context: Inventory control and distribution are key processes in the loss of both efficiency and effectiveness in the field of logistics at the global level. According to the Colombian National Planning Department, for the year 2020, the items of transportation, storage, and inventory account for 73,9% of the total logistics costs. Solving the multi-vehicle Inventory Routing Problem (IRP) is an alternative to making cycle times shorter, more flexible, and less expensive. Method: This article describes and compares mathematical models in the literature for the basic problem, adapting it to its multi-vehicle variant and solving it by means of mixed-integer programming models, via the solution of instances of low and medium mathematical complexity, proposing two ways to manage the inventory and three ways to eliminate the creation of sub-tours. To obtain the results, the AMPL software is used in a computer with an Intel Core i5-5200U CPU@ 2.2 GHz processor and 4 GB RAM, considering a maximum runtime of one hour. Results: The flow model shows the best performance in terms of computational times and response quality regarding the maximum level (ML) policy, and the MTZ variant is the second-best model. Finally, the overall variation exhibits longer execution times and higher GAP values. The models perform well for small-and medium-sized instances. Conclusions: This research presents a general methodology that can be adapted to different applications of the integrated problem of inventory and routing with multiple vehicles. It was verified that the responses generated are of good quality, highlighting the elimination of sub-tours through the flow model and inventory management under the ML policy. Future work should be directed towards finding new alternatives to exact optimization, such as heuristics and metaheuristics, which allow being as close as possible to the optimum in shorter computation times. In addition, stochastic demands could be considered, as well as the handling of perishable products, among others.